Three Perils for a Quest(ion), Part 3

“Things are finally slowing down.  You folks got an interesting talk going, mind if I join you?  I got biscotti.”

“Pull up a chair, Eddie.  You know everybody?”

“You and Jeremy, yeah, but the young lady’s new here.”

“I’m Jennie, visiting from England.”

“Pleased to meetcha.  So from what I overheard, we got Jeremy on some kinda Quest to a black hole’s crust.  He’s passed two Perils.  There’s a final one got something to do with a Firewall.”

“One minor correction, Eddie.  He’s not going to a crust, because a black hole doesn’t have one.  Nothing to stand on or crash into, anyway.  He’s headed to its Event Horizon, which is the next best thing.  If you’re headed inward, the Horizon marks the beginning of where it’s physically impossible to get out.”

“Hotel California, eh?”

“You could say that.  The first two Perils had to do with the black hole’s intense gravitational field.  The one ahead has to do with entangled virtual particles.”

“Entangled is the Lucy-and-Ethel thing you said where two particles coordinate instant-like no matter how far apart they are?”

“Good job of overhearing, there, Eddie.  Jeremy, tell him abut virtual particles.”

“Umm, Mr Moire and I talked about a virtual particle snapping into and out of existence in empty space so quickly that the long-time zero average energy isn’t affected.”

“What we didn’t mention then is that when a virtual pair is created, they’re entangled.  Furthermore, they’re anti-particles, which means that each is the opposite of the other — opposite charge, opposite spin, opposite several other things.  Usually they don’t last long — they just meet each other again and annihilate, which is how the average energy stays at zero.  Now think about creating a pair of virtual particles in the black hole’s intense gravitational field where the creation event sends them in opposite directions.”Astronaut and semi-biscotto
“Umm… if they’re on opposite paths then one’s probably headed into the Horizon and the other is outbound. Is the outbound one Hawking radiation?  Hey, if they’re entangled that means the inbound one still has a quantum connection with the one that escaped!”

“Wait on.  If they’re entangled and something happening to one instantaneously affects its twin, but the gravity difference gives each a different rate of time dilation, how does that work then?”

“Paradox, Jennie!  That’s part of what the Firewall is about.  But it gets worse.  You’d think that inbound particle would add mass to the black hole, right?”

“Surely.”

“But it doesn’t.  In fact, it reduces the object’s mass by exactly each particle’s mass.  That ‘long-time zero average energy‘ rule comes into play here.  If the two are separated and can’t annihilate, then one must have positive energy and the other must have negative energy.  Negative energy means negative mass, because of Einstein’s mass-energy equivalence.  The positive-mass twin escapes as Hawking radiation while the negative-mass twin joins the black hole, shrinks it, and by the way, increases its temperature.”

“Surely not, Sy.  Temperature is average kinetic energy.  Adding negative energy to something has to decrease its temperature.”

“Unless the something is a black hole, Jennie.  Hawking showed that a black hole’s temperature is inversely dependent on its mass.  Reduce the mass, raise the temperature, which is why a very small black hole radiates more intensely than a big one.  Chalk up another paradox.”

“Two paradoxes.  Negative mass makes no sense.  I can’t make a pizza with negative cheese.  People would laugh.”

“Right.  Here’s another.  Suppose you drop some highly-structured object, say a diamond, into a black hole.  Sooner or later, much later really, that diamond’s mass-energy will be radiated back out.  But there’s no relationship between the structure that went in and the randomized particles that come out.  Information loss, which is totally forbidden by thermodynamics.  Another paradox.”

“The Firewall resolves all these paradoxes then?”

“Not really, Jennie.  The notion is that there’s this thin layer of insanely intense energetic interactions, the Firewall, just outside of the Event Horizon.  That energy is supposed to break everything apart — entanglements, pre-existing structures, quantum propagators (don’t ask), everything, so what gets through the horizon is mush.  Many physicists think that’s bogus and a cop-out.”

“So no Firewall Peril?”

“Wanna take the chance?”

~~ Rich Olcott

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Three Perils for a Quest(ion), Part 2

Eddie came over to our table.  “Either you folks order something else or I’ll have to charge you rent.”  Typical Eddie.

“Banana splits sound good to you two?”

[Jeremy and Jennie] “Sure.”

“OK, Eddie, two banana splits, plus a coffee, black, for me.  And an almond biscotti.”

“You want one, that’s a biscotto.”

“OK, a biscotto, Eddie.  The desserts are on my tab.”

“Thanks, Mr Moire.”

“Thanks, Sy.  I know you want to get on to the third Peril on Jeremy’s Quest for black hole evaporation, but how does he get past the Photon Sphere?”

“Yeah, how?”

“Frankly, Jeremy, the only way I can think of is to accept a little risk and go through it really fast.  At 2/3 lightspeed, for instance, you and your two-meter-tall suit would transit that zero-thickness boundary in about 10 nanoseconds.  In such a short time your atoms won’t get much out of position before the electromagnetic fields that hold your molecules together kick back in again.”

“OK, I’ve passed through.  On to the Firewall … but what is it?”

“An object of contention, for one thing.  A lot of physicists don’t believe it exists, but some claim there’s evidence for it in the 2015 LIGO observations.  It was proposed a few years ago as a way out of some paradoxes.”

“Ooo, Paradoxes — loverly.  What’re the paradoxes then?”

“Collisions between some of the fundamental principles of Physics-As-We-Know-It.  One goes back to the Greeks — the idea that the same thing can’t be in two places at once.”

“Tell me about it.  Here’s your desserts.”

“Thanks, Eddie.  The place keeping you busy, eh?”

“Oh, yeah.  Gotta be in the kitchen, gotta be runnin’ tables, all the time.”

“I could do wait-staff, Mr G.  I’m thinking of dropping track anyway, Mr Moire, 5K’s don’t have much in common with base running which is what I care about.  How about I show up for work on Monday, Mr G?”

“Kid calls me ‘Mr’ — already I like him.  You’re on, Jeremy.”

“Woo-hoo!  So what’s the link between the Firewall and the Greeks?”

Link is the right word, though the technical term is entanglement.  If you create two particles in a single event they seem to be linked together in a way that really bothered Einstein.”

“For example?”Astronaut and biscotti
“Polarizing sunglasses.  They depend on a light wave’s crosswise electric field running either up-and-down or side-to-side.  Light bouncing off water or road surface is predominately side-to-side polarized, so sunglasses are designed to block that kind.  Imagine doing an experiment that creates a pair of photons named Lucy and Ethel.  Because of how the experiment is set up, the two must have complementary polarizations.  You confront Lucy with a side-to-side filter.  That photon gets through, therefore Ethel should be blocked by a side-to-side filter but should go through an up-and-down filter.  That’s what happens, no surprise.  But suppose your test let Lucy pass an up-and-down filter.  Ethel would pass a side-to-side filter.”

“But Sy, isn’t that because each photon has a specific polarization?”

“Yeah, Jennie, but here’s the weird part — they don’t.  Suppose you confront Lucy with a filter set at some random angle.  There’s only the one photon, no half-way passing, so either it passes or it doesn’t.  Whenever Lucy chooses to pass, Ethel usually passes a filter perpendicular to that one.  It’s like Ethel hears from Lucy what the deal was — and with zero delay, no matter how far away the second test is executed.  It’s as though Lucy and Ethel are a single particle that occupies two different locations.  In fact, that’s exactly how quantum mechanics models the situation.  Quite contrary to the Greeks’ thinking.”

“You said that Einstein didn’t like entanglement, either.  How come?”

“Einstein published the original entanglement mathematics in the 30s as a counterexample against Bohr’s quantum mechanics.  The root of his relativity theories is that the speed of light is a universal speed limit.  If nothing can go faster than light, instantaneous effects like this can’t happen.  Unfortunately, recent experiments proved him wrong.  Somehow, both Relativity and Quantum Mechanics are right, even though they seem to be incompatible.”

“And this collision is why there’s a problem with black hole evaporation?”

“It’s one of the collisions.”

“There’s more?  Loverly.”

~~ Rich Olcott

Reflections in Einstein’s bubble

There’s something peculiar in this earlier post where I embroidered on Einstein’s gambit in his epic battle with Bohr.  Here, I’ll self-plagiarize it for you…

Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Suppose that photon was yellow light, smack in the middle of the optical spectrum.  Its wavelength, about 580nm, says that the single far-away electron gave its spherical wave about 2.1eV (3.4×10-19 joules) of energy.  By the time it hit your eye that energy was spread over an area of a trillion square lightyears.  Your retinal cell’s cross-section is about 3 square micrometers so the cell can intercept only a teeny fraction of the wavefront.  Multiplying the wave’s energy by that fraction, I calculated that the cell should be able to collect only 10-75 joules.  You’d get that amount of energy from a 100W yellow light bulb that flashed for 10-73 seconds.  Like you’d notice.

But that microminiscule blink isn’t what you saw.  You saw one full photon-worth of yellow light, all 2.1eV of it, with no dilution by expansion.  Water waves sure don’t work that way, thank Heavens, or we’d be tsunami’d several times a day by earthquakes occurring near some ocean somewhere.

Feynman diagramHere we have a Feynman diagram, named for the Nobel-winning (1965) physicist who invented it and much else.  The diagram plots out the transaction we just discussed.  Not a conventional x-y plot, it shows Space, Time and particles.  To the left, that far-away electron emits a photon signified by the yellow wiggly line.  The photon has momentum so the electron must recoil away from it.

The photon proceeds on its million-lightyear journey across the diagram.  When it encounters that electron in your eye, the photon is immediately and completely converted to electron energy and momentum.

Here’s the thing.  This megayear Feynman diagram and the numbers behind it are identical to what you’d draw for the same kind of yellow-light electron-photon-electron interaction but across just a one-millimeter gap.

It’s an essential part of the quantum formalism — the amount of energy in a given transition is independent of the mechanical details (what the electrons were doing when the photon was emitted/absorbed, the photon’s route and trip time, which other atoms are in either neighborhood, etc.).  All that matters is the system’s starting and ending states.  (In fact, some complicated but legitimate Feynman diagrams let intermediate particles travel faster than lightspeed if they disappear before the process completes.  Hint.)

Because they don’t share a common history our nebular and retinal electrons are not entangled by the usual definition.  Nonetheless, like entanglement this transaction has Action-At-A-Distance stickers all over it.  First, and this was Einstein’s objection, the entire wave function disappears from everywhere in the Universe the instant its energy is delivered to a specific location.  Second, the Feynman calculation describes a time-independent, distance-independent connection between two permanently isolated particles.  Kinda romantic, maybe, but it’d be a boring movie plot.

As Einstein maintained, quantum mechanics is inherently non-local.  In QM change at one location is instantaneously reflected in change elsewhere as if two remote thingies are parts of one thingy whose left hand always knows what its right hand is doing.

Bohr didn’t care but Einstein did because relativity theory is based on geometry which is all about location. In relativity, change here can influence what happens there only by way of light or gravitational waves that travel at lightspeed.

In his book Spooky Action At A Distance, George Musser describes several non-quantum examples of non-locality.  In each case, there’s no signal transmission but somehow there’s a remote status change anyway.  We don’t (yet) know a good mechanism for making that happen.

It all suggests two speed limits, one for light and matter and the other for Einstein’s “deeper reality” beneath quantum mechanics.

~~ Rich Olcott

Gin And The Art of Quantum Mechanics

“Fancy a card game, Johnny?”
“Sure, Jennie, deal me in.  Wot’re we playin’?”
“Gin rummy sound good?”


Great idea, and it fits right in with our current Entanglement theme.  The aspect of Entanglement that so bothered Einstein, “spooky action at a distance,” can be just as spooky close-up.  Check out this magic example — go ahead, it’s a fun trick to figure out.

Spooky, hey?  And it all has to do with cards being two-dimensional.  I know, as objects they’ve got three dimensions same as anyone (four, if you count time), but functionally they have only two dimensions — rank and suit.gin rummy hand

When you’re looking at a gin rummy hand you need to consider each dimension separately.  The queens in this hand form a set — three cards of the same rank.  So do the three nines.  In the suit dimension, the 4-5-6-7 run is a sequence of ranks all in the same suit.Gin rummy chart

A physicist might say that evaluating a gin rummy hand is a separable problem, because you can consider each dimension on its own. <Hmm … three queens, that’s a set, and three nines, another set.  The rest are hearts.  Hey, the hearts are in sequence, woo-hoo!> 

“Gin!”

If you chart the hand, the run and sets and their separated dimensions show up clearly even if you don’t know cards.

A standard strategy for working a complex physics problem is to look for a way to split one kind of motion out from what else is going on.  If the whole shebang is moving in the z-direction, you can address  the z-positions, z-velocities and z-forces as an isolated sub-problem and treat the x and y stuff separately.  Then, if everything is rotating in the xy plane you may be able to separate the angular motion from the in-and-out (radial) motion.

But sometimes things don’t break out so readily.  One nasty example would be several massive stars flying toward each other at odd angles as they all dive into a black hole.  Each of the stars is moving in the black hole’s weirdly twisted space, but it’s also tugged at by every other star.  An astrophysicist would call the problem non-separable and probably try simulating it in a computer instead of setting up a series of ugly calculus problems.Trick chart

The card trick video uses a little sleight-of-eye to fake a non-separable situation.  Here’s the chart, with green dots for the original set of cards and purple dots for the final hand after “I’ve removed the card you thought of.”  The kings are different, and so are the queens and jacks.  As you see, the reason the trick works is that the performer removed all the cards from the original hand.

The goal of the illusion is to confuse you by muddling ranks with suits.  What had been a king of diamonds in the first position became a king of spades, whereas the other king became a queen.  You were left with an entangled perception of each card’s two dimensions.

In quantum mechanics that kind of entanglement crops up any time you’ve got two particles with a common history.  It’s built into the math — the two particles evolve together and the model gives you no way to tell which is which.

Suppose for instance that an electron pair has zero net spin  (spin direction is a dimension in QM like suit is a dimension in cards).  If the electron going to the left is spinning clockwise, the other one must be spinning counterclockwise.  Or the clockwise one may be the one going to the right — we just can’t tell from the math which is which until we test one of them.  The single test settles the matter for both.

Einstein didn’t like that ambiguity.  His intuition told him that QM’s statistics only summarize deeper happenings.  Bohr opposed that idea, holding that QM tells us all we can know about a system and that it’s nonsense to even speak of properties that cannot be measured.  Einstein called the deeper phenomena “elements of reality” though they’re currently referred to as “hidden variables.”  Bohr won the battle but maybe not the war — Einstein had such good intuition.

~~ Rich Olcott

Oh, what an entangled wave we weave

“Here’s the poly bag wiff our meals, Johnny.  ‘S got two boxes innit, but no labels which is which.”
“I ordered the mutton pasty, Jennie, anna fish’n’chips for you.”
“You c’n have this box, Johnny.  I’ll take the other one t’ my place to watch telly.”

<ring>
” ‘Ullo, Jennie?  This is Johnny.  The box over ‘ere ‘as the fish.  You’ve got mine!”


In a sense their supper order arrived in an entangled state.  Our friends knew what was in both boxes together, but they didn’t know what was in either box separately.  Kind of a Schrödinger’s Cat situation — they had to treat each box as 50% baked pasty and 50% fried codfish.

But as soon as Johnny opened one box, he knew what was in the other one even though it was somewhere else.  Jennie could have been in the next room or the next town or the next planet — Johnnie would have known, instantly, which box had his meal no matter how far away that other box was.

By the way, Jennie was free to open her box on the way home but that’d make no difference to Johnnie — the box at his place would have stayed a mystery to him until either he opened it or he talked to her.

Entangled 2Information transfer at infinite speed?  Of course not, because neither hungry person knows what’s in either box until they open one or until they exchange information.  Even Skype operates at light-speed (or slower).

But that’s not quite quantum entanglement, because there’s definite content (meat pie or batter-fried cod) in each box.  In the quantum world, neither box holds something definite until at least one box is opened.  At that point, ambiguity flees from both boxes in an act of global correlation.

There’s strong experimental evidence that entangled particles literally don’t know which way is up until one of them is observed.  The paired particle instantaneously gets that message no matter how far away it is.

Niels Bohr’s Principle of Complementarity is involved here.  He held that because it’s impossible to measure both wave and particle properties at the same time, a quantized entity acts as a wave globally and only becomes local when it stops somewhere.

Here’s how extreme the wave/particle global/local thing can get.  Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

cats-eye nebula

The Cat’s Eye Nebula (NGC 6543)
courtesy of NASA’s Hubble Space Telescope

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Surely there was at least one other being, on Earth or somewhere else, that was looking towards the nebula when that wave passed by.  They wouldn’t have seen your photon nor could you have seen any of theirs.  Somehow your wave’s entire spherical shell, all 1012 square lightyears of it, instantaneously “knew” that your eye’s electron had extracted the wave’s energy.

But that directly contradicts a bedrock of Einstein’s Special Theory of Relativity.  His fundamental assumption was that nothing (energy, matter or information) can go faster than the speed of light in vacuum.  STR says it’s impossible for two distant points on that spherical wave to communicate in the way that quantum theory demands they must.

Want some irony?  Back in 1906, Einstein himself “invented” the photon in one of his four “Annus mirabilis” papers.  (The word “photon” didn’t come into use for another decade, but Einstein demonstrated the need for it.)  Building on Planck’s work, Einstein showed that light must be emitted and absorbed as quantized packets of energy.

It must have taken a lot of courage to write that paper, because Maxwell’s wave theory of light had been firmly established for forty years prior and there’s a lot of evidence for it.  Bottom line, though, is that Einstein is responsible for both sides of the wave/particle global/local puzzle that has bedeviled Physics for a century.

~~ Rich Olcott

Think globally, act locally. Electrons do.

“Watcha, Johnnie, you sure ‘at particle’s inna box?”
“O’course ’tis, Jennie!  Why wouldn’t it be?”
“Me Mam sez particles can tunnel outta boxes ’cause they’re waves.”

“Can’t be both, Jessie.”


Double slit experiment

The double-slit experiment.
An electron beam travels from the source at left to a display screen. In between there’s a barrier with two narrow slits.

Maybe it can.

Nobel-winning (1965) physicist Richard Feynman said the double-slit experiment (diagrammed here) embodies the “central mystery” of Quantum Mechanics.

When the bottom slit is covered the display screen shows just what you’d expect — a bright area  opposite the top slit.

When both slits are open, the screen shows a banded pattern you see with waves.  Where a peak in a top-slit wave meets a peak in the bottom-slit wave, the screen shines brightly.  Where a peak meets a trough the two waves cancel and the screen is dark.  Overall there’s a series of stripes.  So electrons are waves, right?

But wait.  If we throttle the beam current way down, the display shows individual speckles where each electron hits.  So the electrons are particles, right?

Now for the spooky part.  If both slits are open to a throttled beam those singleton speckles don’t cluster behind the slits as you’d expect particles to do.  A speckle may appear anywhere on the screen, even in an apparently blocked-off region.  What’s more, when you send out many electrons one-by-one their individual hits cluster exactly where the bright stripes were when the beam was running full-on.

It’s as though each electron becomes a wave that goes through both slits, interferes with itself, and then goes back to being a particle!

By the way, this experiment isn’t a freak observation.  It’s been repeated with the same results many times, not just with electrons but also with light (photons), atoms, and even massive molecules like buckyballs (fullerene spheres that contain 60 carbon atoms).  In each case, the results indicate that the whatevers have a dual character — as a localized particle AND as a wave that reacts to the global environment.

Physicists have been arguing the “Which is it?” question ever since Louis-Victor-Pierre-Raymond, the 7th Duc de Broglie, raised it in his 1924 PhD Thesis (for which he received a Nobel Prize in 1929 — not bad for a beginner).  He showed that any moving “particle” comes along with a “wave” whose peak-to-peak wavelength is inversely proportional to the particle’s mass times its velocity.  The longer the wavelength, the less well you know where the thing is.

I just had to put numbers to de Broglie’s equation.  With Newton in mind, I measured one of the apples in my kitchen.  To scale everything, I assumed each object moved by one of its diameters per second.  (OK, I cheated for the electron — modern physics says it’s just a point, so I used a not-really-valid classical calculation to get something to work with.)

“Particle” Mass, kilograms Diameter, meters Wavelength, meters Wavelength, diameters
Apple 0.2 0.07 7.1×10-33 1.0×10-31
Buckyball 1.2×10-24 1.0×10-9 0.083 8.3×10+7
Hydrogen atom 1.7×10-27 1.0×10-10 600 6.0×10+12
Electron 9.1×10-31 3.0×10-17 3.7×10+12 1.2×10+29

That apple has a wave far smaller than any of its hydrogen atoms so I’ll have no trouble grabbing it for a bite.  Anything tinier than a small virus is spread way out unless it’s moving pretty fast, as in a beam apparatus.  For instance, an electron going at 1% of light-speed has a wavelength only a nanometer wide.

Different physicists have taken different positions on the “particle or wave?” question.  Duc de Broglie claimed that both exist — particles are real and they travel where their waves tell them to.  Bohr and Heisenberg went the opposite route, saying that the wave’s not real, it’s only a mathematical device for calculating relative probabilities for measuring this or that value.  Furthermore, the particle doesn’t exist as such until a measurement determines its location or momentum.  Einstein and Schrödinger liked particles.  Feynman and Dirac just threw up their hands and calculated.

Which brings us to the other kind of quantum spookiness — “entanglement.”  In fact, Einstein actually used the word spukhafte (German for “spooky”) in a discussion of the notion.  He really didn’t like it and for good reason — entanglement rudely collides with his own Theory of Relativity.  But that’s another story.

~~ Rich Olcott